Information processing apparatus, server apparatus, and computer program product

ABSTRACT

In an embodiment, an information processing apparatus is connected to external apparatuses. The information processing apparatus includes:
     a device key storage unit configured to store a device key; a shared key storage unit configured to store one or more shared keys shared by the external apparatuses; a key generating unit configured to generate a media key from the device key and media key blocks; and an updating unit configured to generate the shared keys as generated shared keys, which is updated, based upon the media key and the shared keys stored in the shared key storage unit, and to store the generated shared keys into the shared key storage unit.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. application Ser. No.13/431,215, filed on Mar. 27, 2012, and is based upon and claims thebenefit of priority from Japanese Patent Application No. 2011-158398,filed on Jul. 19, 2011, the entire contents of which are incorporatedherein by reference.

FIELD

Embodiments described herein relate generally to an informationprocessing apparatus, a server apparatus, and a computer programproduct.

BACKGROUND

A technique of IKE (Internet Key Exchange) has been known as a techniqueof performing a two-way authentication and sharing an encryption keybetween two devices (information processing apparatuses). There arebasically two methods in this technique; a method based upon a publickey cryptosystem, and a method based upon a pre-shared key.

The method based upon the public key cryptosystem is excellent inreducing cost for a key management, but computation cost increases. Themethod based upon the pre-shared key is excellent in reducingcomputation cost, but cost for the key management increases. Forexample, under a situation in which a device is subject to attack, andhence, secret information is leaked, the method based upon the publickey cryptosystem can easily reconstruct the system. On the other hand,the method based upon the pre-shared key needs much cost for thereconstruction of the system.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram illustrating a system according to anembodiment;

FIG. 2 is a block diagram of a KDC;

FIG. 3 is a block diagram illustrating an updating unit;

FIG. 4 is a sequence diagram illustrating an updating process in theembodiment;

FIG. 5 is a view illustrating a graph structure managing a device and apre-shared key;

FIG. 6 is a view illustrating a graph structure managing a device and apre-shared key;

FIG. 7 is a view of a tree structure when the device is revoked; and

FIG. 8 is a view illustrating a hardware structure of the deviceaccording to the embodiment.

DETAILED DESCRIPTION

In an embodiment, an information processing apparatus is connected toexternal apparatuses. The information processing apparatus includes: adevice key storage unit configured to store a device key; a shared keystorage unit configured to store one or more shared keys shared by theexternal apparatus; a key generating unit configured to generate mediakeys from the device key and media key blocks; and an updating unitconfigured to generate the shared keys as generated shared keys, whichis updated, based upon the media keys and the shared keys stored in theshared key storage unit, and to store the generated shared keys into theshared key storage unit.

Exemplary embodiments of the information processing apparatus will beexplained below in detail with reference to the accompanying drawings.

The information processing apparatus according to an embodiment providesan efficient updating function of a pre-shared key with a method basedupon a pre-shared key, thereby realizing a reduction in cost for a keymanagement. The information processing apparatus updates all pre-sharedkeys, retained by a device having no information leakage, by using theupdating function of the pre-shared key. The information processingapparatus also sets a device, to which a predetermined updatedpre-shared key is assigned, instead of the device having the informationleakage. With this, the system can efficiently be reconstructed, even ifan attacker illegally obtains the device.

The information processing apparatus (device) according to the presentembodiment uses an MKB (media key block) that can derive (generate) amedia key, which is suitable for calculating a pre-shared key used in apredetermined key exchange system. The MKB is distributed to each devicefrom a key distribution center (KDC). Each device generates the mediakey from the MKB and a device key of the device, and generates a newpre-shared key by using the generated media key and the pre-shared key.

A typical device key includes plural sets of secret keys (CS (CompleteSub-tree method, etc.)). The way of constructing the device key isdetermined according to the employed MKB system.

In the embodiment described below, a device employs one set of devicekeys and one pre-shared key. The device may employ plural sets of devicekeys and plural pre-shared keys. Such embodiments described above can berealized by applying the process similar to the process that isperformed in the embodiment below to one of the plural sets of devicekeys and to one of the plural pre-shared keys.

Increasing the number of the key components held by the device makes itpossible for plural systems to manage plural pre-shared keys held by onedevice, whereby more flexible key management can be realized withoutdeteriorating efficiency.

Therefore, it is unnecessary to distribute the pre-shared key to eachdevice from a key management server, which is conventionally performed,upon updating the pre-shared key. Specifically, the KDC only distributesthe common MKB to each device. In order to revoke a certain device, theKDC only re-distributes the common MKB that is updated to revoke thedevice. Specifically, each device can update the pre-shared key, and thedevice can easily be revoked, only by the distribution of the MKB by theKDC.

FIG. 1 is a block diagram illustrating one example of the configurationof the system according to the present embodiment. As illustrated inFIG. 1, the system according to the present embodiment includes pluraldevices 100 a and 100 b serving as the information processing apparatus,and a KDC 10 serving as a server apparatus, those of which are connectedwith network 20. Any network systems such as the Internet can be appliedto the network 20.

The devices 100 a and 100 b have the same configuration. Therefore, theyare merely referred to as a device 100, when it is unnecessary todistinguish the device 100 a from the device 100 b. The device 100 isnot limited to two. The system may be configured to include three ormore devices 100.

The KDC 10 generates the media key, generates the MKB, and distributesthe MKB. FIG. 2 is a block diagram illustrating an example of theconfiguration of the KDC 10. As illustrated in FIG. 2, the KDC 10includes a reception unit 11, a transmission unit 12, an MKB generatingunit 13, and a key storage unit 14.

The reception unit 11 receives various data pieces from an apparatussuch as the device 100. The transmission unit 12 transmits various datapieces to the apparatus such as the device 100. For example, thetransmission unit 12 transmits the MKB generated by the MKB generatingunit 13 to the device 100. The method of inputting the MKB to the device100 is not limited thereto. For example, the MKB may be input to thedevice 100 via a storage medium having the MKB stored therein.

The key storage unit 14 stores the device key assigned to each device100, and a shared key that is shared by each device 100. The key storageunit 14 stores all device keys in the MKB system.

The MKB generating unit 13 generates the MKB by using the device key.Any methods such as CS (Complete Sub-tree method, SD (Subset Difference)method, or LKH (Logical Key Hierarchy) method are applied to the methodof generating the MKB.

A public key KP for a signature validation is applied to the KDC 10 aspublic information. The KDC 10 holds a secret key KS for the public keyKP for the signature as secret information that only the KDC 10 knows. Apublic key and secret key of a digital signature using an elliptic curvecan be used as the public key KP and the secret key KS, for example.

Returning to FIG. 1, at least one device key is assigned to each device100. The KDC 10 gives a bit string x with a predetermined length or moreas the media key of the MKB. The x is the bit string selected by the KDC10. The bit string x is referred to as the media key x below.

After receiving the MKB, each device 100 processes the MKB by the devicekey assigned to each device 100 so as to acquire the media key x. Inthis case, when the device 100 is revoked by the MKB, this device 100cannot correctly process the MKB, resulting in that the device 100cannot correctly acquire the media key x.

Each device 100 holds a pre-shared key that is shared by the otherdevice that is the communication destination. For example, the device100 a and the device 100 b hold a pre-shared key psk.

The device 100 includes an MKB processing unit 110, a shared key storageunit 120, an updating unit 130, and a communication unit 140.

The MKB processing unit 110 stores (memorizes) the device key of thedevice 100. For example, the MKB processing unit 110 in the device 100 areads the distributed MKB. When the device key of the device 100 a isnot revoked, the MKB processing unit 110 can generate the media key xfrom the MKB. The MKB processing unit 110 sends the generated media keyx to the updating unit 130.

The updating unit 130 receives the pre-shared key psk, which is sharedby the device 100 b, from the shared key storage unit 120. The updatingunit 130 generates a new pre-shared key psk2 by using the pre-shared keypsk and the media key x. The updating unit 130 stores the updatedpre-shared key psk2 into the shared key storage unit 120 as a newpre-shared key psk. The updating unit 130 may delete the pre-shared keypsk that has been stored before the update from the shared key storageunit 120. The shared key storage unit 120 sends the pre-shared key pskto the communication unit 140, according to need. The communication unit140 executes an authenticated key exchange protocol to makecryptographic communication.

The MKB processing unit 110 may be configured to confirm the signatureof the MBK in order to prevent the forgery of the MKB. In this case, theKDC 10 generates a digital signature corresponding to the MKB by use ofthe public key KS in order to show the validity of the MKB, andtransmits the digital signature together with the MKB. The MKBprocessing unit 110 stores the public key KP of the KDC 10, and confirmsthe signature of the MKB by use of the public key KP.

The MKB processing unit 110 may transmit a version number of the MKB tothe communication unit 140. The version number of the MKB is data withthe order accompanied by the MKB. The communication unit 140 mayexchange the version number before performing the key exchange operationwith the device 100 b. The communication unit 140 does not exchange thekey with the device that has an older number of the key version. In thiscase, the communication unit 140 may perform data exchange to the device100 b so as to confirm whether the shared key can correctly be shared bythe device 100 b.

The detailed configuration of the MKB processing unit 110 will bedescribed next. As illustrated in FIG. 1, the MKB processing unit 110includes a device key storage unit 111, and a key generating unit 112.

The device key storage unit 111 stores the device key assigned to thedevice 100. The key generating unit 112 reads the MKB, processes the MKBwith the device key stored in the device key storage unit 111, andgenerates the media key x. The key generating unit 112 sends thegenerated media key x to the updating unit 130. In this case, a mediakey storage unit (not illustrated) may be provided to store the mediakey x generated by the key generating unit 112 into the media keystorage unit. In this case, the media key storage unit may send themedia key x to the updating unit 130 according to the request from theupdating unit 130.

The detailed configuration of the updating unit 130 will be describednext. FIG. 3 is a block diagram illustrating an example of theconfiguration of the updating unit 130. As illustrated in FIG. 3, theupdating unit 130 includes a public information storage unit 131, and akey calculating unit 132.

The public information storage unit 131 stores a cryptographic hashfunction H such as SHA family that is cryptographically secure as a keyderivation function.

The key calculating unit 132 calculates the updated pre-shared key psk2that is updated from the media key x received from the MKB processingunit 110, the pre-shared key psk received from the shared key storageunit 120, and the hash function H received from the public informationstorage unit 131.

The key derivation function used for calculating the updated pre-sharedkey is not limited to the hash function H. Any key derivation functionscan be applied, so long as they calculate by use of the media key x andthe pre-shared key. For example, a pseudorandom function or a one-wayfunction other than the hash function may be used. If the pseudorandomfunction is used, it is difficult to estimate the updated pre-shared keywithout the acquisition of the media key x, even in the case ofunauthorized release of the pre-shared key.

The hash function H used for calculating the updated pre-shared keythrough an input of two variables, which are the media key x and thepre-shared key psk, has been described above. However, a function forcalculating the shared key through an input of two or more variables maybe used.

For example, the updated pre-shared key may be calculated from two mediakeys and one pre-shared key calculated from two MKBs. When these MKBsare issued from different management systems, the function of updatingthe pre-shared keys can be divided into two systems. Alternatively, twopre-shared keys may be calculated from one MKB and two pre-shared keyscalculated from one MKB. In this way, one management system cancollectively manage the pre-shared keys corresponding to pluralfunctions.

The above-mentioned examples are only illustrative. Even in a case whereplural MKBs and plural pre-shared keys are used, the calculation caneasily be realized by applying the system according to the presentembodiment.

The key exchange system by the communication unit 140 can be realized byan authenticated key exchange system using the pre-shared key in theNon-Patent Document 1 of “RFC2409, The Internet Key Exchange (IKE)”, D.Harkins et al., [online], November 1998, retrieved from the Internet:<URL: http://www.ietf.org/rfc/rfc2409.txt> or in the Non-Patent Document2 of “RFC4306, The Internet Key Exchange (IKEv2) Protocol”, C. Kaufman,[online], December 2005, retrieved from the Internet: <URL:http://www.ietf.org/rfc/rfc4306.txt>. The key exchange system by thecommunication unit 140 is not limited to the systems described in theNon-Patent Document 1 above or the Non-Patent Document 2 above. Anysystems that can utilize the pre-shared key can be applied.

The communication unit 140 may regard the media key x as the pre-sharedkey, and perform the authenticated key exchange. In this case, the keyexchange system by the communication unit 140 is an anonymousauthenticated key exchange system in which the key exchange is made withthe authentication based only on the fact that the device is notrevoked.

Each of the pre-shared keys is not necessarily set independently. It mayhave a dependence relationship with a graph structure such as a treestructure. Each of the pre-shared keys may have a dependencerelationship calculated from a graph structure used for generating theMKB.

The respective storage units (device key storage unit 111, shared keystorage unit 120, public information storage unit 131, key storage unit14) may be realized by any storage mediums widely used, such as HDD(Hard Disk Drive), an optical disk, a memory card, and RAM (RandomAccess Memory).

The updating process of the pre-shared key by the device 100 thusconfigured according to the present embodiment will be described withreference to FIG. 4. FIG. 4 is a sequence view illustrating the flow forupdating the pre-shared key by the device 100. The case where thepre-shared key of the device 100 is updated will be described below asone example.

The MKB generating unit 13 in the KDC 10 firstly generates the MKB byusing information (revoke device information) for specifying revokeddevices out of the devices 100 and the device keys of the devices 100(step S101). The KDC 10 then generates a signature of the generated MKBby using the secret key KS (step S102). The transmission unit 12 in theKDC 10 distributes the MKB and the generated signature to each device100 (step S103).

The MKB processing unit 110 in the device 100 validates the signature ofthe MKB by using the public key KP (step S104). When the signature doesnot pass the validation, the following process is stopped.

The key generating unit 112 in the device 100 processes the MKB by usingthe device key stored in the device key storage unit 111 to generate themedia key x (step S105). When the MKB process cannot be executed, theprocess is stopped, since the device 100 is revoked.

The updating unit 130 in the device 100 generates the updated pre-sharedkey psk2 that is generated from the hash function H, the media key x,and the pre-shared key psk (step S106).

The shared key storage unit 120 in the device 100 stores the psk2 as psk(step S107).

Similarly, the validation of the signature of the MKB, the generation ofthe media key x, the generation of the updated pre-shared key, and thestorage of the updated pre-shared key are executed in the other device100.

Modification 1

In the modification 1, the KDC 10 manages one graph structure that isformed by combining a graph structure involved with the generation ofthe MKB and a graph structure involved with the management of thepre-shared key.

FIG. 5 is a view illustrating one example of the graph structuremanaging the device and the pre-shared key. The KDC 10 manages thedevice key (in this example, k1 . . . k15) for generating the MKB byutilizing the tree-structured graph such as CS system or SD system.Specifically, the KDC 10 manages the device key in association with eachnode (second node) included in the graph. The KDC 10 generates thepre-shared key corresponding to each device 100 from the device key (inthis example, k8 . . . k15) corresponding to leaves of the differenttree structures for each device 100. The KDC 10 manages the pre-sharedkey in association with each node (first node) coupled from the leaf ofthe graph in chains.

The specific process will be described. The KDC 10 holds two types ofpseudorandom functions f and g. The KDC 10 randomly generates k1, andthen, recursively generates the following device keys, such as k2=f (k1,0), k3=f (k1, 1) . . . k15=f (k7, 1). Specifically, when the keycorresponding to the child node at the left of the tree structure isdefined as kj, the key corresponding to the child node at the right isdefined as kj+1, and the key corresponding to their parent is defined aski, the equations of kj=f(ki, 0), and kj+1=f(ki, 1) are established.

Then, the KDC 10 selects mk1, which is a random value, so as to generatethe pre-shared keys psk1 . . . psk8, such as psk1=h(mk1, k8),psk2=h(mk1, k9) . . . psk8=h(mk1, k15).

The KDC 10 allows the device 100 having the device key including k8 andthe device 100 that makes the authenticated key exchange with the device100 to hold the psk1. The KDC 10 makes such assignment according to theconfiguration of the system.

For example, when the device 100 including k8 in the device key and thedevice 100 including k10 in the device key make the authenticated keyexchange, each device 100 generates the pre-shared key psk from psk1 andpsk3 by a predetermined method, and use the IKE based upon thepre-shared key, whereby they can make the key exchange.

The pre-shared key is updated by using the common media key x acquiredthrough the process to the MKB as in the above-mentioned embodiment.

With this management, the KDC 10 only stores the device keycorresponding to the root of the tree structure and a generation rule ofthe media key x used for generating the pre-shared key. Therefore, theinformation that should be managed can safely be reduced.

The management in FIG. 5 is only illustrative, and the management may bemade with any optional graph structures such as a tree structureillustrated in FIG. 6, for example. The KDC 10 may not send the same MKBto all devices, but send partial information of the MKB according to thedevice.

The specific example will be described with reference to the conditionin FIG. 7. FIG. 7 illustrates one example of the tree structure when thedevice 100 including the device key k10 is revoked. When the MKB isgenerated in the CS system, the MKB includes three encrypt data, whichare encrypt data encrypted with k4, encrypt data encrypted with k11, andencrypt data encrypted with k3. In a normal CS system, the MKB includingall of three encrypt data pieces are sent to all devices. However, inthis system, each device 100 receives useless data that is not neededfor the reconstruction of its device key.

Therefore, the KDC 10 may send the partial information of the MKBaccording to the device 100 to which the MKB is distributed. Forexample, only the encrypt data encrypted with k4, out of the encryptdata included in the MKB, is sent to the device 100 including the devicekey k8. The partial information of the corresponding MKB may be sentaccording to the inquiry (request) from the device 100.

One example of distributing the partial information of the MKB in the CSsystem under the condition in FIG. 7 will be described. The device 100including k13 sends the information including an ID, by which the device100 can be identified as the device including k13, to the KDC 10. Here,any IDs are used, so long as they can associate the device 100 with thetree structure, such as a character string, a lot number, or a number ofa node of a tree structure, assigned to each device 100 beforehand bythe KDC 10. After receiving the ID of the device 100 including k13, theKDC 10 sends the encrypt data encrypted with k3 out of encrypt datacontained in the MKB as the partial information of the MKB that cancorrectly be processed by the device 100 including k13.

Another example of distributing the partial information of the MKB inthe CS system under the condition in FIG. 7 will be described. Thedevice 100 including k8 sends the information including an ID, by whichthe device 100 can be identified as the device including k2, to the KDC10. Here, any IDs are used, so long as they can associate the device 100with the tree structure, such as a character string, a lot number, or anumber of a node of a tree structure, assigned to each device 100beforehand by the KDC 10. After receiving the ID of the device 100including k2, the KDC 10 sends the encrypt data encrypted with k4 andthe encrypt data encrypted with k11 out of encrypt data contained in theMKB as the partial information of the MKB that can correctly beprocessed by the device 100 including k2. When the device 100 makes aninquiry of the MKB to the KDC 10, the ID that should be sent to the KDC10 by the device 100 may be restricted to the information associatedwith a node at a predetermined height in the tree structure.

Next, one example of a method of sending the MKB will be described. Anetwork certification system called Kerberos certification is widelyused. The Kerberos certification will briefly be described below.

In the Kerberos certification, a client who receives the service makesan access to a KDC (hereinafter referred to as KKDC (Kerberos KDC) thatexecutes the Kerberos certification, and reports a server of the servicethe client intends to enjoy. The client and the KKDC preliminarily sharea (symmetrical) key, and the KKDC certifies the client by using thiskey. The KKDC sends two data pieces called tickets to the client. One isthe ticket for the client, and the other is the ticket for the server.The ticket for the KKDC is encrypted by the shared key by the KKDC andthe client. The client decodes his/her ticket, and takes out a sessionkey with the server from the decoded data. The client also sends to theserver the ticket for the server. The ticket for the server is encryptedby the shared key of the server and the KKDC. The server decodes itsticket, and takes out the session key with the client from the decodeddata. From the procedure above, the client and the server can share thesession key. When the client requests the service to the server, theserver can certify the client by use of the session key.

It is supposed that the server and the client share a shared key psk0.The shared key psk0 is intended to be updated by using the Kerberoscertification. It is supposed that the server and the clientrespectively hold a device key. It is also supposed that thepredetermined expiration date is set on the psk0.

The ticket for the Kerberos certification has a field ofauthorization-data. The KKDC stores in this field of the ticket the MKBthat encrypts the media key x, and the expiration date of a key (definedas psk1) that is obtained by updating the psk0. For example, it issupposed that the client makes communication using the psk0 with theserver. The client confirms the expiration date of the psk0. If it isvalid, the client makes the communication using the psk0.

However, if the psk0 is no longer valid, the client accesses to the KKDCto receive a ticket. The client decodes his/her ticket to take out theMKB, and processes the MKB with the device key of the client. When theclient is not revoked, the client acquires the media key x. The clientupdates the psk0 by using the media key x: psk1←H(x, psk0). The clientalso sets the new expiration date included in the ticket as theexpiration date of the psk1. Then, the client sends to the server aticket for the server.

After receiving the ticket for the server from the client, the serverdecodes this ticket to take out the MKB, and processes the MKB with thedevice key of the server. When the server is not revoked, the serveracquires the media key x. The server updates the psk0 by use of themedia key x: psk1←H(x, psk0). The server also sets the new expirationdate included in the ticket as the expiration date of the psk1.

As described above, the shared key psk0 shared by the client and theserver can be updated. By the similar procedure, the shared key of theclient and the server can be distributed to the client and the server.In this case, the updating procedure is not performed in both the clientand the server, but the obtained media key x is only set as the sharedkey psk between the client and the server; psk←x.

As described above, the information processing apparatus according tothe present embodiment can realize the authenticated key exchange systemthat can achieve efficient computation cost and key management cost.

The hardware structure of each device (device and KDC) will next bedescribed with reference to FIG. 8. FIG. 8 is an explanatory viewillustrating the hardware structure of the apparatus according to thepresent embodiment.

The apparatus according to the present embodiment includes a controldevice such as a CPU (Central Processing Unit) 51, a storage device suchas a ROM (Read Only Memory) 52 and a RAM (Random Access Memory) 53, anI/F 54 that makes communication through the connection to the network,an external storage device such as HDD (Hard Disk Drive) or CD (CompactDisc) drive device, a display apparatus such as a display device, aninput apparatus such as a keyboard or mouse, and a bus 61 thatinterconnects the respective units. The system has a hardware structureutilizing a general computer.

A program executed in the apparatus according to the present embodimentis recorded on a computer-readable recording medium such as CD-ROM(Compact Disk Read Only Memory), flexible disk (FD), CD-R (Compact DiskRecordable), or DVD (Digital Versatile Disk) in an installable form orexecutable form, and provided as a computer program product.

The program executed in the apparatus according to the presentembodiment may be stored on a computer connected to the network such asthe Internet, and provided as being downloaded through the network. Theprogram executed in the apparatus according to the present embodimentmay be provided or distributed through the network such as the Internet.

The program according to the present embodiment may be provided as beinginstalled on the ROM beforehand.

The program executed in the information processing apparatus (device)according to the present embodiment has a module structure including theabove-mentioned respective units (MKB processing unit, updating unit).The program executed in the server apparatus (KDC) according to thepresent embodiment has a module structure including the above-mentionedrespective units (reception unit, transmission unit, MKB generatingunit). As an actual hardware, the CPU 51 (processor) reads and executesthe program from the storage medium, whereby the respective units areloaded on the main storage device to be generated thereon.

While certain embodiments have been described, these embodiments havebeen presented by way of example only, and are not intended to limit thescope of the inventions. Indeed, the novel embodiments described hereinmay be embodied in a variety of other forms; furthermore, variousomissions, substitutions and changes in the form of the embodimentsdescribed herein may be made without departing from the spirit of theinventions. The accompanying claims and their equivalents are intendedto cover such forms or modifications as would fall within the scope andspirit of the inventions.

What is claimed is:
 1. A server apparatus connected to pluralinformation processing apparatuses, comprising: processing circuitryconfigured to operate as a generator that generates first informationbased upon keys associated with at least one of nodes included in atree-structured graph; a receiver that receives a node ID identifyingone of the nodes; and a transmitter that transmits, to an informationprocessing apparatus, partial information that is only a part of thefirst information and that is generated by only a first key among thekeys, the first key being associated with a node included in a subtreein which a root node is the node identified by the node ID or the firstkey corresponding to a root node of a subtree that includes the nodeidentified by the node ID.
 2. The server apparatus according to claim 1,wherein the first information is used to generate a shared key that isshared by the plural information processing apparatuses.
 3. A serverapparatus connected to plural information processing apparatuses,comprising: a receiver that receives a node ID identifying one of nodesincluded in a tree-structured graph; and a transmitter that transmits,to an information processing apparatus, partial information that is onlya part of first information and that is generated by only a first keyamong the keys, the first information being generated based upon keysassociated with nodes included in a tree-structured graph, the first keybeing associated with a node included in a subtree in which a root nodeis the node identified by the node ID or the first key corresponding toa root node of a subtree that includes the node identified by the nodeID.
 4. The server apparatus according to claim 3, wherein the firstinformation is used to generate a shared key that is shared by theplural information processing apparatuses.
 5. A server apparatusconnected to plural information processing apparatuses, comprising: akey storage that stores one or more shared keys shared among the pluralinformation processing apparatuses, in association with a first node,the first node being associated with a leaf of a tree-structured graph;and processing circuitry configured to operate as a generator thatgenerates first information block based upon first keys that areassociated with second nodes included in the tree-structured graph, thefirst keys being generated based upon second keys that are associatedwith a root node of the tree-structured graph; and a transmitter thattransmits, to an information processing apparatus, partial informationthat is only a part of the first information and that is generated byonly a third key among the first keys, the third key being associatedwith a node included in a subtree in which a root node is the nodeidentified by the node ID or the third key corresponding to a root nodeof a subtree that includes the node identified by the node ID.